Goals from the red-headed midfielder either side of the break and Shefki Kuqi's second of the season gave Neil Warnock's men a comfortable 3-0 win to stretch Palace's unbeaten run to four and to throw the Tykes further into the early season relegation mire.
And the home side fully deserved their third three-point haul on the bounce after a dominant display which suggests their early-season stutters are truly behind them.
Palace started brightly with Watson and Craig Beattie both going close during the early exchanges, before Nick Carle missed a superb chance flashing wide from 12 yards after the Tykes rearguard failed to deal with a Watson corner.
After a lull, Palace finally took the lead in the 25th minute when Victor Moses was brought down in the box by keeper Heinz Muller after Stephen Foster made a hash of Julian Speroni's long goal kick and Watson made no mistake to put Palace ahead.
On-loan Scotland striker Beattie then went inches from doubling Palace's lead three minutes later when his firm header from another Watson corner flew just over the bar.
Barnsley started the second period brightly and Maceo Rigters should have put the Tykes level a minute after the restart when Palace failed to deal with an out-swinging Diego Leon free-kick, but the Dutchman's snapshot from 10 yards flew straight to the grateful Speroni.
Seconds later, Watson shaved Muller's right-hand post with a 25-yard piledriver before Anderson and Jamal Campbell-Ryce missed decent opportunities.
Tykes playmaker Leon played in Iain Hume with a beautiful pass in the 52nd minute only for the Canadian to be denied with a superbly timed challenge from Clint Hill.
And Palace made Davey's men pay for their missed chances on the hour after Carle's neat cut back from the left found the unmarked Watson, who made no mistake from close range.
Palace completed their comfortable victory in the 82nd minute when Foster misjudged another lengthy Speroni kick to let in substitute Kuqi, who coolly lifted the ball over the stranded Muller.